CTF: Capture the Flag.
Mode 1: Players kill each other on any territory, always respawn at home base, and attempt to take the flag.
Mode 2: No respawn; killed players are dead. Otherwise, identical.
Mode 3: Only people who are on the opposing side may be hurt. Players have a "jail" and a "jail guard'.
D & D: Destroy and Defend. One force defends a complex, the other tries to destroy it.
Easter Egg Hunting: You hunt down and kill, destroy or take an objective: easter eggs, zerglings, psychos....
Mode 1: You must be the first to take a certain number of objects.
Mode 2: There is a time limit, and you must have the most at the end.
Endurance/Survival Rounds: Fight as long as you can while the GM throws every he's got at you. Poor, poor you.
Other Orders
And, the order can be spontaneous.
Environmental Damage: Players are looking to cause the most damage to the environment. Players may be killed by other players, which is a great way for people who don't have area effect weapons to win.
Hide and Go Seek: An evil version of the original, in which the hiders are going to be killed by the seeker. The hiders can attack their enemies and kill them, but they cannot compromise their position there, or they're next.
"It" Survival: You, the "it", survive for as long as you can before you get gunned down like the animal you are. The other three versions differ beyond this point.
Mode 1: The "it" is killed for good. It is slightly unfair, because the third "it" has two less players to run from than the fifth "it".
Mode 2: The it is revived and then fights the next "it".
King of the Kill: Similar to the Duke Nukem "King of the Hill", people fight up to a certain set number of kills. The first killer gets the "King", and if a King is killed, the killer gets the "King" designation and five kills instead of one.
King of the Hill: Like the old schoolyard game, except with automatic weapons!
Presidente/Bodyguard: In this scenario, one player character is "the president". He must be protected at all costs. A few players are the Secret Service Agents enlisted to protect him. The rest are all assassins who want to kill the president.
Racing: Players race each other on foot around a track. The person to make all the laps is the winner, but the last person standing will be the winner by default. This changes the playing field, because the person who would normally win the race (due to superior endurance or strength) now must deal with his enemies firing sniper rifles and fireballs at him.
Regular: People just take their characters and fight to kill.
Reverse Endurance Rounds: Another single-player battle arena. Players must fight one beefed up warrior. They are given some characters to fight with. In this scenario, players develop the abilities to utilize an unknown character's capacities, the ability to keep losses down (which is what prizes are rewarded for), and (in Choose mode) the ability to make wise choices.
Choose: Choose your enemy and your team.
Spontaneous: The GM makes up spontaneously.
Set: You fight in a set order.
Team Endurance: People run through endurance rounds on a team.
Team-on-one Battle: Players fight en masse against a very powerful force; i.e. Thing in the Cave, a T-1000, an Agent...
Team vs. Team: There are two flavors of this.
One player team vs. one player team: Let's say two characters control big forces or lots of characters. The two forces can fight in this form.
Many player team vs. many player team: Players divide into two teams. They choose their one character and fight with their team against the opposing team.
Tournament: The tournament players face off one-on-one or two-on-two in any mode, eliminating people until one is left.
Mode 1: In this one, one loss loses you the tournament.
Mode 2: Players count their wins and losses and win there.
I think some prize condition information can help.
